Published in Petroleum Transactions, AIME, Volume 216, 1959, pages 321–323. Abstract Simplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations as those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Under certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equation. This equation is analogous to the equation for the pressure in single-phase compressible flow. The analysis reveals that the equation for the pressure in multiphase flows can be obtained directly from the equation for the pressure in single-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphase flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. Introduction One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered.
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John C. Martin (1959) studied this question.